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Ida Ariska
Universitas Jember
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Analisis Rainbow Vertex Connection pada Beberapa Graf Khusus dan Operasinya Ida Ariska; Dafik Dafik; Ika Hesti Agustin
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (295.31 KB) | DOI: 10.25037/cgantjma.v2i1.53

Abstract

Suppose $G=(V(G),E(G))$ is a non-trivial connected graph with edge coloring defined as $c:E(G) \rightarrow \{1,2,...,k\} ,k \in N$, with the condition that neighboring edges can be the same color. An original path is {\it rainbow path} if there are no two edges in the path of the same color. The graph $G$ is called rainbow connected if every two vertices in $G$ with rainbow path in $G$. The coloring here is called rainbow coloring, and the minimal coloring in a graph $G$ rainbow connection number is denoted by $rc(G)$. Suppose $G=(V(G),E(G))$ is a non-trivial connected graph with a vertex coloring defined as $c':V(G) \rightarrow \{1,2,...,k\},k \in N$, with the condition that neighboring interior vertex may have the same color. An original path is rainbow vertex path if there are no two vertices in the path of the same color. The graph $G$ is called rainbow vertex connected if every two vertices in $G$ with rainbow vertex path in $G$. The $G$ coloring is called rainbow vertex coloring, and the minimal coloring in a $G$ graph is called rainbow vertex connection number which is denoted by $rvc(G)$. This research produces rainbow vertex connection number on the graph resulting from the operation \emph{amal}($Bt_{m}$, $v$, $n$), $Wd_{3,m}$ $\Box$ $ P_n$, $P_m$ $\odot$ $Wd_{3,n}$, $Wd_{3,m}$ $+$ $C_n$, and \emph{shack}($Bt_{m}$, $v $, $n$). 
Analisis rainbow vertex connection pada beberapa graf khusus dan operasinya Ida Ariska; Ika Hesti Agustin; Kusbudiono Kusbudiono
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 3, No 1 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25037/cgantjma.v3i1.78

Abstract

The vertex colored graph G is said rainbow vertex cennected, if for every two vertices are connected by a path whose internal vertices have distinct colors. The rainbow vertex connection number of G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainbow vertex connected. On this research, will be raised the issue of how to produce graphs the results of some special graph and how to find the rainbow vertex connection. Operation that use cartesian product, crown product, and shackle. Theorem in this research rainbow vertex connection number in graph the results of operations Wd3,m □ Pn,,Wd3,m ⵙ Pn, and shack(Btm,v,n).
Co-Authors D. Dafik Ika Hesti Agustin, Ika Hesti Kusbudiono Kusbudiono, Kusbudiono